Related papers: Bernstein-Sato theory for arbitrary ideals in posi…
We show that Stanley's conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.
In this paper we obtain some statements concerning ideals of polynomials and apply these results in a number of different situations. Among other results, we present new characterizations of $\mathcal{L}_{\infty}$-spaces, Coincidence…
We define a class of Bernstein-Szeg\H{o} measures on $\mathbb{R}^2$ and we establish their spectral properties, providing a natural extension of the one-dimensional theory. We also derive conditions involving finitely many moments, which…
M. Morales introduced a family of binomial ideals that are binomial extensions of square free monomial ideals. Let $I\subset \si$ be a square free monomial ideal and $J\subset\sis$ a sum of scroll ideals with some extra conditions, we…
A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associated with some sumset semigroups is provided. Using these…
The characterization of permutations over finite fields is an important topic in number theory with a long-standing history. This paper presents a systematic investigation of low-degree bivariate polynomial systems $F=(f_1(x,y),f_2(x,y))$…
Let $ f_i: X \rightarrow {\bf C}$, for $i$ integer between $ 1$ and $ p $, be analytic functions defined on a complex analytic variety $X$. Let us consider $ {\cal D}_X $ the ring of linear differential operators and $ {\cal D}_X [s_1,…
We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…
Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally…
In this paper, we introduce the notion of a characteristic-zero lifting of an object in positive characteristic by means of ``skeletons''. Using this notion, we relate invariants of singularities in positive characteristic to their…
Mayr and Meyer found ideals with the doubly exponential ideal membership property. In the analysis of the associated primes of these ideals (in math.AC/0209344), a new family of ideals arose. This new family is presented and analyzed in…
In this thesis we investigate certain types of monomial ideals of polynomial rings over fields. We are interested in minimal free resolutions of these ideals (or equivalently the quotients of the polynomial ring by the ideals) considered as…
The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…
We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical…
We give all bi-unitary non splitting even perfect polynomials over the prime field of two elements, which are divisible by Mersenne irreducible polynomials raised to special exponents. We also identify all bi-unitary perfect polynomials…
For $j=1,2$, let $f_j(z) = \sum_{n=1}^{\infty} a_{j}(n) e^{2\pi i nz}$ be a holomorphic, non-CM cuspidal newform of even weight $k_j \ge 2$ with trivial nebentypus. For each prime $p$, let $\theta_{j}(p)\in[0,\pi]$ be the angle such that…
We provide a formula for $F$-thresholds of a Thom-Sebastiani type polynomial over a perfect field of prime characteristic. This result extends the formula for the $F$-pure threshold of a diagonal hypersurface. We also compute the first test…
Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case.…
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…
Let B be a commutative B\'ezout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable sets in terms, on one hand, of the definable sets in the…